Superconducting Resonator Research Articles

High-Cooperativity Coupling of Electron-Spin Ensembles to Superconducting Cavities

Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many qubits could be encoded into spin waves of a single ensemble. We demonstrate the coupling of electron-spin ensembles to a superconducting transmission-line cavity at strengths greatly exceeding the cavity decay rates and comparable to the spin linewidths. We also perform broadband spectroscopy of ruby (Al₂O₃:Cr(3+)) at millikelvin temperatures and low powers, using an on-chip feedline. In addition, we observe hyperfine structure in diamond P1 centers.

Design and Fabrication of a Tunable Superconductive Resonator Utilizing Micromachined Tunable Capacitor

This paper presents the design, fabrication, and characterizations of a flip-chip-bonded micromachined capacitor for tuning a high-temperature superconductive resonator. The major issue of the tunable superconductive resonator is its high driving voltage due to the accumulated thermal stresses and the sensitivity of the superconductive material to the fabrication process. The tunable capacitor in the form of a microbridge with flexible boundaries is proposed to reduce thermal stress. Thermal stress is reduced to 10 MPa, and the pull-in voltage of the capacitor is 25 V. The micromachined capacitor and the superconductive resonator are fabricated separately and then integrated together by using a flip-chip-bonding technique. This integration method prevents the superconductor material from the high-temperature process. At 75-K operation temperature, the measured center frequency of the fabricated tunable resonator changes from 2.93 to 2.87 GHz when the driving voltage increases from 0 to 40 V.

Superconducting twin quarter wave resonator for acceleration of low velocity heavy ions

We have designed and fabricated a superconducting twin quarter wave resonator (Twin-QWR) made of niobium and copper for the acceleration of low velocity heavy ions. The resonator has two inner conductors and three acceleration gaps, which give a resonant frequency of 129.8 MHz and an optimum beam velocity of 6% of the light velocity. Each inner conductor resonates like in a coaxial quarter-wave line resonator. The resonator was designed to have a separable structure so that we could treat the inner conductor's part fully made of high purity niobium apart from the outer conductor made of niobium and copper. We obtained an acceleration field gradient of 5.8 MV/m at an RF power input of 4 W.

Noise in a superconducting single-electron transistor resonator driven by an external field

We investigate the noise properties of a superconducting single-electron transistor (SSET) coupled to a harmonically driven resonator. Using a Langevin equation approach, we calculate the frequency spectrum of the SSET charge and calculate its effect on the resonator field. We find that the heights of the peaks in the frequency spectra depend sensitively on the amplitude of the resonator oscillation and hence suggest that the heights of these peaks could act as a sensitive signal for detecting the small changes in the amplitude of the drive. The previously known results for the effective amplitude-dependent damping and temperature provided by the SSET for the case of a low-frequency resonator are generalized for all resonator frequencies.

Entangled States in a Single-Qubit Structure with SQUID Coupled with a Super-conducting Resonator

In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a single-qubit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.

Modeling Superconducting Transmission Line Bends and Their Impact on Nonlinear Effects

This paper reports on a numerical technique to obtain the current distribution in the annular bent sections of planar layouts. This is used to obtain the linear and nonlinear circuit distributed parameters modeling a superconducting strip bend and its impact on intermodulation distortion. As an example, we analyze a superconductive open-loop resonator and assess the linear and nonlinear contribution of its bends in its overall linear and nonlinear performance. These simulations are very useful for optimizing the resonators of a filter in order to minimize its nonlinear distortion

Physics design of the 8 GeV H-minus linac

The proposed 8 GeV proton driver (PD) linac at FNAL is based on 436 independently phased superconducting (SC) resonators (Foster and MacLachlan 2002 Proc. LINAC-2002 p 826). The linac includes a front end up to ∼420 MeV and a high energy section operating at 325 and 1300 MHz respectively. A room temperature (RT) radio frequency quadrupole (RFQ) and short H-type resonators are proposed for the initial acceleration of the H-minus or proton beam up to 10 MeV. From 10 to ∼420 MeV the voltage gain is provided by SC spoke-loaded cavities. In the high-energy section, the acceleration is provided by the International Linear Collider (ILC)-style SC elliptical cell cavities. The beam physics and the lattice design for the FNAL 8 GeV linac are discussed in this paper.

Nonlinear Model of Coupled Superconducting Lines

High Temperature Superconductor materials are known to produce intermodulation and other nonlinear effects. In planar structures, these nonlinearities depend on the field configuration on the strip, which in turn strongly depends on the device structure and therefore on the coupling between the strips. In this work we present an equivalent circuit that models the linear and nonlinear effects in coupled transmission lines. Numerical techniques based on Harmonic Balance are used to solve the equivalent circuit. We validate the equivalent circuit model by fitting measurements of a superconducting hairpin notch resonator. Examples of several coupled transmission line structures are given.

Superconducting microwave resonator for millikelvin magnetic resonance force microscopy

We have fabricated a superconducting resonator capable of generating a strong microwave magnetic field in a small (100 μm) volume for low temperature magnetic resonance experiments. While the resonator was specifically developed for use at millikelvin temperatures in a dilution refrigerator, where the total cooling power is limited to a few hundred microwatts, it is also useful at temperatures up to 5 K. The resonator consists of a 220 μm diameter, 2-1/2 turn niobium coil resonating with a short section of niobium microstripline. At a resonance frequency of 3 GHz, the loaded Q of the resonator was 780. The field strength was characterized by performing electron spin nutations. Operating at 100 mK with 320 μW of dissipated power, the resonator generated a field of 4 G at a distance of 100 μm from the coil.

A controller for 97 MHz super-conducting QWR for NSC LINAC booster

A resonator controller has been implemented to stabilize the amplitude and phase of rf fields in the super-conducting resonators of NSC LINAC. Due to reduced losses these resonators have intrinsic band width of the order of 0.1 Hz at 97 MHz whereas the vibration-induced center frequency changes are of the order of a few tens of hertz. In the control strategy followed, the resonator is made the frequency selective part of an oscillator. The phase lock is achieved by dynamically adding a phase shift in the oscillator. A slow tuner minimizes the slow drifts in the resonator center frequency. In this paper we present the control strategy, implementation details and performance obtained with this controller.

Characteristics of mechanically tunable superconductive resonators

In order to realize superconductive microwave devices with large tuning characteristics, we have studied a mechanically tunable superconductive resonator beneath a dielectric and/or magnetic floating plate (FP) as a first step. The resonator consists of a half-wavelength coplanar waveguide (CPW). The principle of the mechanically tunable method is that variations of the effective permittivity and/or the effective permeability for the microwave waveguide line can be obtained by changing the distance between the resonator and the FP. In computer simulations of electromagnetic fields for the mechanically tunable half-wavelength CPW resonator, we have obtained a large shift of the resonant frequency with a band of 1.75 GHz to 7 GHz (tunability is approximately 25%) using the (La0.3Sr0.7)(Al0.65Ta0.35)O3 (LSAT) single crystal (dielectric constant (εr) = 22.8, loss tangent (tanδ) = 1.7 × 10−4) as the FP. Based on the results, we have performed an experiment using a half-wavelength CPW resonator made from YBa2Cu3O7−δ thin film and the LSAT FP. The result shows a drastic resonant frequency shift of approximately 1.36 GHz (tunability is approximately 20%) when the LSAT FP is moved, using an electromagnetic actuator. In this experiment, it is also noted that the insertion loss is quite low, less than 0.8 dB, compared to previous reports for various tunable filters. Moreover, we have also measured the tuning characteristics with a TiO2 single crystal (εr = 85.4, tanδ = 2.5 × 10−4) as the FP. As a result, we have obtained quite large tuning characteristics of approximately 2 GHz (tunability is approximately 28%).

Simulation of Microwave Losses of Superconductive Microstrip Line Resonators and Filters Using Commercial Software

The microwave losses of double-sided superconducting YBa2Cu3O7 − x thin films is presented. The films were grown on both sides of LaAlO3 substrates. The microstrip resonators and the filters were patterned and etched using the technique of photolithography. The performance of high frequency microstrip resonator was studied for a resonance frequency of 5 GHz and for a temperature range of 17–100 K. The power dependence of the quality factor measured and the shift in the resonant peak with respect to temperature are also reported. We performed simulations using two phenomenological models. These models were confirmed by our experimental results. Several commercial software were used in our simulations, with appropriate modifications. We were able to reproduce our experimental results using the models mentioned above. The physical parameters used in the model were chosen from among those reported and accepted in literature. In order to validate these models we designed a band-pass filter. Theoretical simulation was performed on a two-pole filter using the models mentioned above. Then two real filters have been prepared using the technique of photolithography. Experimental measurements have been performed on these filters. Comparison between the experimental and simulation results are presented. The goal of this paper is to demonstrate that it is possible to use commercial software to design planar microwave devices by performing only few appropriate modifications.

Active tuning of high frequency resonators and filters

In this paper, we present a new electromechanical approach of active control of high temperature superconducting (HTS) resonator and filter center frequency. The design of the tunable devices incorporates piezoelectric bender or tube actuator, which acts as a varactor of the resonance circuit, with YBCO thin film on LAO substrate. The resonator has an unloaded Q of over 18,000 at 77 K and a center frequency of 362 MHz and a tuning range of over 20% with unloaded Q over 10,000. By applying different voltages to the piezoelectric bender, we have tuned the resonance frequency over 30% with a good linearity and high Q. Based on this structure, a two-pole HTS bandpass filter was designed, fabricated and tested. The filter has a tunable center frequency from 17 to 20 MHz while maintaining a 2.5% 3dB bandwidth, and an insertion loss of less than 0.5 dB at 77 K.

Simplified method for measurements and calculations of coupling coefficients and Q/sub 0/ factor of high-temperature superconducting dielectric resonators

To accurately determine the surface resistance of high-temperature superconducting films, multifrequency measurements of S/sub 21/, S/sub 11/, and S/sub 22/ and sophisticated data processing are required. As a result, surface resistance measurements and calculations for varying temperatures are very time consuming. In this paper, we introduce a simplified method for calculations of the unloaded Q (Q/sub 0/) factor, which require measurements of S/sub 11/ and S/sub 22/ at the lowest temperature only. For all other temperatures, only S/sub 21/ measurements are needed. The method has been shown to give sufficiently accurate Q/sub 0/ values and, hence, the surface resistance of superconducting samples, as compared to results obtained from S/sub 21/, S/sub 11/, and S/sub 22/ measurements using the transmission-mode Q factor technique. The presented method has been tested under different coupling coefficients and frequencies.

Dual-mode helical resonators

High performance and compact size are the most important criteria in filter-based products for satellite communication systems. Succeeding the superconducting and dielectric resonators, the conventional single-mode helical resonator ranks favorably on its high unloaded-Q per volume. Improvement of the performance has been demonstrated by operating the helical resonator at a higher order (n>0) mode. In addition, these resonators can also be fabricated onto a high dielectric-constant material to further reduce the size of the filter structure. Detailed design considerations of the dual-mode wire-wound helical resonator filter, as well as implementation of the dual-mode dielectrically loaded helical resonator filter structure, are presented in this paper.

Current density and power handling of high-temperature superconductive thin film resonators and filters

This paper presents experimental and theoretical results for a number of high-temperature superconductive (HTS) planar thin film filters and resonators. The circuits were manufactured using TBCCO films. The measured maximum power handled by each assembled filter and resonator was correlated with the maximum normalized current density predicted by a commercially available software package. The results achieved were used to deduce the critical current density in each HTS device. The data demonstrates that it is possible to predict the power-handling capability of new filter designs by analyzing the results of the current density simulation. Manufacturing and testing resources can thus be limited to those HTS circuit designs which show the greatest potential for high-power handling.

Frequency stable superconducting resonator with buffer layers

The resonant frequency of a superconducting planar resonator is dependent on the material properties and thicknesses of the superconductors, the dielectric (substrate), and the buffer layers. In this article, we compute the first and second derivatives with respect to temperature of a wave velocity ratio (with respect to free space) for various combinations of material properties. The dependence of resonant frequency on the dielectric constant and thicknesses of the substrate and buffer layers is discussed. An example of YBCO thin films on rutile with sapphire buffer layers was computed. From this example, it may be concluded that, if a turning point can be realized at T=60 K and the temperature controlled to better than 0.1 mK, then frequency standards with stabilities of parts in 1015 should be attainable.

Diagnostics of the high-T/sub c/ superconductive films in a strong electromagnetic field

The method for diagnostics of the nonlinear properties of the high-T/sub c/ superconductive films is proposed. It employs the experimentally obtained nonlinear radiocharacteristics of a superconductive resonator and takes into account the inhomogeneous distribution of the nonlinear surface impedance, caused by inhomogencity of the RF-magnetic field amplitude along a film surface. The last circumstance leads to the integral equation for surface impedance of a superconductor. The proposed method is based on solution of the inverse problem of electrodynamics. The dependences of surface resistance on the RF-magnetic field amplitude, and relationships between precision of the method and a measurement error are obtained.

An X-band HEMT microwave oscillator stabilized with a superconducting resonator

A parallel feedback oscillator using a transmission-type high-temperature superconducting (HTS) resonator is designed and implemented in hybrid technology. A (Tl-2212) microstrip resonator on an substrate is integrated with a two-stage PHEMT amplifier. The oscillator is tested at 12.3 GHz and demonstrates phase noise of at 100 kHz offset from the carrier and a stability of at 77 K.

Magnetically tunable YBaCuO microstrip resonators and bandpass filters

We report experimental results on frequency tuning in superconductive resonators and bandpass filters with controlling magnetic fields. The frequency shifts are attributed to the presence of vortices modifying the microwave penetration depth and therefore the kinetic inductance of the circuit. 7-pole microstrip filters with a center frequency of 14 GHz and a bandwidth of 4% were fabricated using YBaCuO films deposited on MgO substrate with Au ground plane. A negative frequency shift of −12 MHz for fields lower than 0.1 mT was observed at 40 K.